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Circular motion with friction and banking - resultant forces

  1. Jun 22, 2007 #1

    exi

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    1. The problem statement, all variables and given/known data

    A car travels 76 m/s around a circular track with a 111 m radius.

    The car's mass is 2500 kg, the track is angled at 21°, and the coefficient of friction is 0.18.

    What is the magnitude of the resultant force on the car and driver, expressed as kN?

    3. The attempt at a solution

    Double-checking my work here to see if I'm understanding this correctly.

    If:
    Fk = µ*Fn
    Fn = mg/cosΘ
    Fc = mv²/r

    Then:
    Fc = 130090.09 N
    Fk = 4723.75 N

    Which leaves me with two questions: Is the above correct, and what am I leaving out of the forces before summing them?

    editing this to add: I've gotten a series of formulas that produce the correct answer, but I do not know where they are derived from. If anyone could help explain this, I'd appreciate it.

    1. [tex]A = \frac {m(v^2cos\theta - grsin\theta)}{r}[/tex]

    2. [tex]B = \frac {mg + Asin\theta}{cos\theta}[/tex]

    3. [tex](\mbox{Answer expressed in kN}) = \frac {Acos\theta + Bsin\theta}{1000}[/tex]
     
    Last edited: Jun 22, 2007
  2. jcsd
  3. Jun 23, 2007 #2
    You're going around your butt to get to your elbow. ;-)

    If an object is moving in uniform circular motion, the NET force on that object must be equal to (mv^2)/r. You have this value recorded as Fc. You should note that Fc is NOT a single force, but rather is the NET force on the object in question.

    The three formulas you've listed end up spitting out the exact same value as Fc, although in a very convoluted way.
     
  4. Jun 23, 2007 #3

    exi

    User Avatar

    Oh wow, you're right - what I did in the first 30 seconds answered the problem, but I didn't know I actually had the answer. I had to call someone in class with me who was given that formula system by a physics tutor.

    That's... definitely something. :shy:
     
  5. Oct 26, 2011 #4
    hallo exi may you explain the set of fomulas listed below the senteces in red...@all...i have a problem in calculatiion of forces in a free body diagram...any body who can help?
     
  6. Oct 26, 2011 #5
    We have to start from a FBD.

    Try to find the forces which act on the car.
     
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